Rešite 50*10^{3}=(9*10^9)(80*10^66)(-6*10^-6)/r^2

$$50 \times 10 ^ { 3 } = \frac { ( 9 \times 10 ^ { 9 } ) ( 80 \times 10 ^ { 66 } ) ( - 6 \times 10 ^ { - 6 } ) } { r ^ { 2 } }$$

Rešitev za r

$$r=-2400000000000000000000000000000000\sqrt{15}i\approx -0-9,295160031 \cdot 10^{33}i$$

$$r=2400000000000000000000000000000000\sqrt{15}i\approx 9,295160031 \cdot 10^{33}i$$

Koraki za iskanje kvadratnega korena

Spremenljivka r ne more biti enaka vrednosti 0, ker deljenje z vrednostjo nič ni določeno. Pomnožite obe strani enačbe s/z r^{2}.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 9 in 66, da dobite 75.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 75 in -6, da dobite 69.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Izračunajte potenco 10 števila 3, da dobite 1000.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Pomnožite 50 in 1000, da dobite 50000.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Izračunajte potenco 10 števila 69, da dobite 1000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Pomnožite 9 in 1000000000000000000000000000000000000000000000000000000000000000000000, da dobite 9000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Pomnožite 9000000000000000000000000000000000000000000000000000000000000000000000 in 80, da dobite 720000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

Pomnožite 720000000000000000000000000000000000000000000000000000000000000000000000 in -6, da dobite -4320000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

Delite obe strani z vrednostjo 50000.

$$r^{2}=\frac{-4320000000000000000000000000000000000000000000000000000000000000000000000}{50000}$$

Delite -4320000000000000000000000000000000000000000000000000000000000000000000000 s/z 50000, da dobite -86400000000000000000000000000000000000000000000000000000000000000000.

$$r^{2}=-86400000000000000000000000000000000000000000000000000000000000000000$$

Enačba je zdaj rešena.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$

Koraki z uporabo formule za reševanje kvadratne enačbe

Spremenljivka r ne more biti enaka vrednosti 0, ker deljenje z vrednostjo nič ni določeno. Pomnožite obe strani enačbe s/z r^{2}.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 9 in 66, da dobite 75.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 75 in -6, da dobite 69.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Izračunajte potenco 10 števila 3, da dobite 1000.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Pomnožite 50 in 1000, da dobite 50000.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Izračunajte potenco 10 števila 69, da dobite 1000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Pomnožite 9 in 1000000000000000000000000000000000000000000000000000000000000000000000, da dobite 9000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Pomnožite 9000000000000000000000000000000000000000000000000000000000000000000000 in 80, da dobite 720000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

Pomnožite 720000000000000000000000000000000000000000000000000000000000000000000000 in -6, da dobite -4320000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

Dodajte 4320000000000000000000000000000000000000000000000000000000000000000000000 na obe strani.

$$50000r^{2}+4320000000000000000000000000000000000000000000000000000000000000000000000=0$$

Ta enačba je v standardni obliki: ax^{2}+bx+c=0. Vstavite 50000 za a, 0 za b in 4320000000000000000000000000000000000000000000000000000000000000000000000 za c v formulo za reševanje kvadratnih enačb \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Kvadrat števila 0.

$$r=\frac{0±\sqrt{-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Pomnožite -4 s/z 50000.

$$r=\frac{0±\sqrt{-200000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Pomnožite -200000 s/z 4320000000000000000000000000000000000000000000000000000000000000000000000.

$$r=\frac{0±\sqrt{-864000000000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Uporabite kvadratni koren števila -864000000000000000000000000000000000000000000000000000000000000000000000000000.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{2\times 50000}$$

Pomnožite 2 s/z 50000.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}$$

Zdaj rešite enačbo r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}, ko je ± plus.

$$r=2400000000000000000000000000000000\sqrt{15}i$$

Zdaj rešite enačbo r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}, ko je ± minus.

$$r=-2400000000000000000000000000000000\sqrt{15}i$$

Enačba je zdaj rešena.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$